Multiple Cash Flows FVyou have:bank account that earns 8% interest$7,000 in bank nowyou:deposit $4,000 at end of each of next 3 yearsHow much at the end of 3 years?

Multiple Cash Flows FV-7,000.00-4,000.00-4,000.00-4,000.00?FV0+FV1+FV2+FV3PV0 = -7,000.00PV1 = -4,000.00PV2 = -4,000.00PV3 = -4,000.00t0 =t1 =t2 =t3 =3210

Multiple Cash Flows FV-7,000.00-4,000.00-4,000.00-4,000.00FVPV0 = -7,000.00PV1 = -4,000.00PV2 = -4,000.00PV3 = -4,000.00t0 =t1 =t2 =t3 =3210

Multiple Cash Flows FVyou have:mutual fund that earns 9% interestinvest $500 nowanother $600 in 1 yearHow much at the end of 2 years?What if you leave it in for 5 years?

-500.00Multiple Cash Flows FVPV0012FVHow much at the end of 2 years?-600.00PV1

-500.00Multiple Cash Flows FVPV0012345FV-600.00PV1How much at the end of 5 years?FV

Multiple Cash Flows FVyou have:account the earns 8% interestinvest $100 at year 1another $300 at year 3How much at the end of 5 years?

-100.00Multiple Cash Flows FVPV0012345-300.00PV1r =.08FV

Multiple Cash Flows PVyou are offered an investment that pays$200 at year 1another $400 at year 2another $600 at year 3another $800 at year 4you can earn 12% on similar investmentsHow much is this investment worth today?

Multiple Cash Flows PV01234r =.12$200.00FV1$400.00FV2$600.00FV3$800.00FV4PV0

Multiple Cash Flows PVYou are considering an investment that pays$1,000 at year 1another $2,000 at year 2another $3,000 at year 3If you want to earn 10% on your money, how much should you be willing to pay?

Multiple Cash Flows PV0123r =.10$1,000.00FV1$2,000.00FV2$3,000.00FV3PV0

Multiple Cash Flows PVyoure CEO of small printing companyyou want to make profits at least 10%.your staff tell youif you buy a used printing machine for $5,000it will make profits of:$1,000 at the end of year 1another $2,000 at the end of year 2another $3,000 at the end of year 3machine will be worthless after year 3Should you buy the machine?

Multiple Cash Flows PV0123r =.10$1,000.00FV1$2,000.00FV2$3,000.00FV3PV0$5,000?

Multiple Cash Flows PVyour staff have a new idea:buy a machine for $100,000will make$40,000 profit at the end of year 1$75,000 profit at the end of year 2after year 2again, machine value = $0this is a lot of money, so you want15% return

Multiple Cash Flows PV012r =.15$40,000.00FV1$75,000.00FV2PV0$100,000?

Fri

Saving For Retirementyou are offered opportunity to put some money away for retirement you will receive5 annual payments $25,000 eachbeginning in 40 years How much would you be willing to invest today if you desired an interest rate of 12%?simplify

Saving For Retirement5 annual payments$25,000.00 eachbeginning in 40 yearsinterest rate of 12%how much willing to invest?simplifychart

Saving for RetirementPV0chartr =.12

Perpetuities & Annuitiespayments at regular intervalsAnnuitya finite seriesordinary annuitypayment at end of each periodannuity due payment at beginning of each periodPerpetuityan infinite series

Perpetuity PVWhat?Co.preferred stock$500.00 dividend every yearinterest rate of comparable investment8.00%PV =present price=?c =dividend every period=500.00r =interest=.0800

Perpetuity PVWhat?Co.wants to issue preferred stockdesired price$100.00dividend of ?Why?Co.has a preferred stockcurrent price$40.00dividend of $1.00 every quarterr = 2.50%/quarterc = $2.50/quarter

Growing Perpetuity PVWhat?Co.preferred stock$500.00 dividend every yeardividend grows every year6.00%comparable interest8.00%

AnnuitiesFuture Value annuity factorPresent Value annuity factor

Annuity PV500.00FV1PV500.00FV2500.00FV3r = 10%PV = $1,243.43

Annuity PVCadillac Escaladeloan payments $632.00/monthbank terms1%/month48 monthsHow much can you borrow?PV = $23,999.54

Annuity PVPublishers Clearinghouse$10 million prizepaid30 equal annual installments$333,333.33 eachif PC can borrow money at 5%how much does it actually cost them?PV = $5,124,150.29

Annuity cFinding the Paymentwant to borrow $20,000 8% per yearcompounded monthly 4-year loanc = -$488.26

Annuity tborrow$2,000.00at 5.00%annual payments$734.42How long before you pay off the loan?solving for tt = 3.00

Annuities FVSaving for retirement$2,000.00/year 7.50% interest rateHow much will you have in 40 years?

Growing Annuity PV

Growing Annuity PV$50,000-a-year jobincrease by 5.00%/yearretire in 40 years8.00% interest rateWhat is the present value of this job?

EAREffective Annual RateWhich savings account is better?15.0%compounded daily15.5%compounded quarterly16.00%compounded annuallym = # times interest compounded during the year

APR

CorpFi ApplicationsAnnuitiescapital spendingrational pricelease or buyPrinting machine$1,000.00 profit/year for 10 yearsWhat should we pay?

CorpFi ApplicationsAnnuitiescapital spendingrational pricelease or buyPrinting machinewhich is betterbuy for $6,000.00?lease for $800.00/year?

CorpFi ApplicationsGrowing AnnuitiesWhat should my company be worth?rational priceProfitthis year made$16,000growing at 3%/yearalternative: 7.5%/year

CorpFi ApplicationsAnnuitiesrational pricestockcommonpreferredbonds

5.*5.*5.*Calculator:30 N; 5 I/Y; 333,333.33 PMT; CPT PV = 5,124,150.295.*Note if you do not round the monthly rate and actually use 8/12, then the payment will be 448.30

Calculator:4(12) = 48 N; 20,000 PV; .66667 I/Y; CPT PMT = 488.265.*Sign convention matters!!!5 I/Y2000 PV-734.42 PMT CPT N = 3 years5.*FV = 2000(1.07540 1)/.075 = 454,513.04

Remember the sign convention!!!40 N7.5 I/Y-2000 PMTCPT FV = 454,513.045.*5.*